Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol’skii–Besov spaces

2021 ◽  
Vol 252 (4) ◽  
pp. 508-525
Author(s):  
Anatolii Sergiiovych Romanyuk ◽  
Viktor Sergiiovych Romanyuk
2020 ◽  
Vol 17 (3) ◽  
pp. 372-395
Author(s):  
Anatolii Romanyuk ◽  
Viktor Romanyuk

We have obtained the exact-order estimates for some approximative characteristics of the Sobolev classes $\mathbb{W}^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}$ and Nikоl'skii--Besov classes $\mathbb{B}^{\boldsymbol{r}}_{p,\theta}\ $ of periodic functions of one and several variables in the norm of the space $B_{\infty, 1}$. Properties of the linear operators realizing the orders of the best approximation for the classes $\mathbb{B}^{\boldsymbol{r}}_{\infty, \theta}$ in this space by trigonometric polynomials generated by a set of harmonics with $``$numbers$"$ from step hyperbolic crosses are investigated.


1982 ◽  
Vol 56 (4) ◽  
pp. 524-528 ◽  
Author(s):  
Joseph Th. J. Tans ◽  
Dick C. J. Poortvliet

✓ The pressure-volume index (PVI) was determined in 40 patients who underwent continuous monitoring of ventricular fluid pressure. The PVI value was calculated using different mathematical models. From the differences between these values, it is concluded that a monoexponential relationship with a constant term provides the best approximation of the PVI.


1995 ◽  
Vol 42 (2) ◽  
pp. 367-378 ◽  
Author(s):  
M. Mateljević ◽  
M. Pavlović

2021 ◽  
Vol 15 ◽  
pp. 31
Author(s):  
S.V. Babenko ◽  
V.I. Ruban

We investigate the interrelations between the error of one method of curve approximation and the error of the best approximation.


2020 ◽  
pp. 130-158
Author(s):  
Lea Raible

Moving from the conceptual to the substantive, this chapter refines our account of jurisdiction based on a concept of power and argues that it is best understood as political power in particular, as opposed to coercion. I argue that political power in this context should be conceptualised to denote the ability of public institutions to determine how individual powers are transformed. That is, political power is the ability of public institutions to mediate the abilities of individuals into a different set of abilities. As such, it is constitutive of and necessary for public institutions, it affects individuals because it provides the very framework for them to pursue their lives in equality, and it is virtually unavoidable. The exercise of political power results in non-exclusive control on particular states of affairs in the area of the rights outlined in any given treaty. The vehicle through which this power is manifested is the choice and application of rules. Political power so understood is the best approximation of a factual position to guarantee equality, which, as we have seen in Chapter 2, is what justifies human rights obligations of public institutions in the first place.


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